I would start by deleting unnecessary files. I do not know if /dev/dsk/c0t3d0s0 contains /tmp or /var/tmp but that is a good place to start.
du -ks *
Will give you size of files and directories. I would concentrate on the largest.
I would kill any users processes that are trying to create files in /dev/dsk/c0t3d0s0.
Once under 100% I would reboot the system

That's a performance response for any UNIX engineer, does not have to be OS
specific.
Start looking into your files that will not be needed and move them or back
them up, that would free you up some space.

Since you are at 100% use you must tar, backup or gzip your files not needed
and store them in a save place

HInga:
Check for core files in /
cd /
find . -name core -exec ls -al {} \;
If any core files are found, move them to a new location or remove them
If there are no core files, check for zip'd or compressed files:
find . -name '*.gz' -exec ls -al {} \;
find . -name '*.Z' -exec ls -al {} \;
There may also be log files hidden somewhere in the / filesystem, but they could be located anywhere.
Good Luck!
Rick.

Yes, the application will freeze when the root (/) file system is filling.
The fact that it's filling at all tends to tell you that an application is
faulting, and filling the logs with complaints about something, or
creating system and/or application core dumps.

SO, you need to halt applications running on the system. Reduce the
running applications as much as possible so that the applications will
not protect their data files, junk files and logs.

Next, go looking for large files. Pay attention to where they are,
and if they are part of a system you don't know about. Google what
you don't know until you are SURE they are not critical.

Next, find all the core files produced by system and applications.
Make sure they are older, and not part of an application system.
SOME people just insist on naming part of their programs core and it
is a good idea to NOT run a find/rm script or command line deletes.

Delete the core files that you can. find the log files, and delete the
older versions, if you are running log file rotation scripts. If you are
confident you know what you are doing, use the cat /dev/null
command, and redirect it with > to any file that looks non-critical.
That should zero it out. When possible, copy the file to another
file space before zeroing it.

Basically, you now have to identify the out-of-control application,
and fix the problem. Start each application, and wait for it to put
entries in system logs, etc. that identify whats wrong.
Merlin5x5
Senior UNIX / ORACLE Systems Engineer

Hi,
First of all, try to remove core files(if you need them, move to other
partition)
Try to compress some unused files(unused files for startup)
try to move some "dot files" under root userid
as you know, there are a lot of "dot files" under every userid.
try to remove/move some backup files like passwd.old passwd.bak.....
you can move some directories(not needed at startup time) to other partition
then create "symbolic link" to those directories